OneCare should not have any problems at all with 1 gig of memory. If your scan is locking up the PC and you are experiencing other issues related to performance, the first thing that I would suspect would be that other security software is still installed fully or partially and is conflicting with OneCare.
If you are unable to identify any conflicting software and the performance issues persist, please contact support.
How to reach support (FAQ) - http://social.microsoft.com/Forums/en-US/onecareinstallandactivate/thread/30400b52-7f26-4ba0-bc18-17e305329d90
-steve
Microsoft MVP Windows Live / Windows Live OneCare & Live Mesh Forum Moderator